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- relative = sensor of displacement + reference point often non-contact- absolute = reference point inside of sensor + rel. sensor of displacement

electrodynamic sensor of vibration (geophone) v piezoelectric (~) and capacitive (=) accelerometers a

Accelerometers for inertial navigationaccelerometers with electromechanical feedback (servo-accelerometers)

Sensors of mechanical vibrationvibration...oscillating motion of body about a reference position

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Absolute sensors of vibrations

m - mass

k - stiffness (spring constant) b viscous friction coefficient

022

=++ kxdt dx

bdt

z d m

z(t) = x(t) + y(t)

2

2

2

2

dt yd mkx

dt dxb

dt xd m =++

Equation of motion of

mass-spring system

presumption:t je) j(Y)t(y =

Solution: )t( je) j(X)t(x =

inertialforce

damping

spring force

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Amplitude frequency response:

Phase frequency response

where:

222

2

)B2()1() j(Y) j(X

+=

21B2arctg

=

0

=

mk

0 =

kr b b

B =

0kr m2 b =

- normalised frequency(referenced to resonance freq.)

- resonant frequency

- damping ratio

- critical damping ratio0 0,20,40,60,8 1 1,21,41,61,8 20

-30

-60

-90

-120

-150

-1800,01

0,5

b)

0,250,1

12

4

B=0

0 0,5 1 1,5 2 2,5 30

1

2

3

4

5

6

2

10,7

0,5

0,3

0,2

0,1

a)

0,4

B=0X jY j

( )( )

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1B,1 >

1B,1

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1

2

3

4

5

y

y

d ydt

2

2

Electrodynamic sensor of vibration

- seismic mass = mass of coil 1 + mass of winding 2

1 - pick-up coil

2 damping winding

5 - membrane

3 cylindrical part of mg. circuit

- viscous damping due to currents induced in winding 2

4 permanent magnet

- induced voltagedt

du

= proportional to the velocity of coil

- universality

GEOPHONE

- application: vibrations of machines, buildings, occupancy detection- cheap f r = 1 .. 100 Hz, m = 20g .. 5 kg

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Absolute sensors of acceleration -Accelerometers- measurement of acceleration for high frequency of vibrations => highresonant frequency of sensor is required

- optimumum - piezoelectric sensors of displacement of seismic mass withrespect to sensor case

large k, small m .

2222 )B2()1(

1) j(Y) j(X1

+=

- amplitude frequency response:

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8 20

0,5

1

1,5

2

0,7070,5

0,33

B=0,2

0

02

2 ( )( )X jY j

- difficulties with stability of damping

solution:insertion of system to liquid

mk

0 =

Ideal response

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shear deformation

+ decreasing the sensitivity to thermal dilatation (deformation of bottom ofsensor case, thermal dilatation, acoustic effects

22

1

34

delta shear accelerometr with shear strain :

1 - platform

2 - segments3 central stick 4 piezoceramics plates

Bruel Kjaer

- seismic mass = ring holder + segments- k stiffness piezoceramic elements

Max. 20 000 g

Piezoelectric accelerometer (~)

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charge amplifier

Problem of piezo-accelerometers:no static response (static charge is drained by leakage)Problems of signal recovery special amplifiers:

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Capacitive accelerometers

- mass spring system = thin membrane with helicalslits and openings

- analogy to viscous damping = pumping of airthrough slits by movement

- location of membrane: between solid electrodes

0.2 .. 1000 g

f r = 20 Hz .. 15 kHz

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Accelerometer with vibrating beam

R 1

R 2

k

y(t)

m

M

k - beamm - seismic mass

-suitable for MEMS technology

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Strain gage accelerometer (=)- air bag system

-thick layer strain gages measures deformation of triangular beam tuned by a mass

- at collision the condition for velocity measurement must be fulfilled- normal drive system must not be activated

mm

tenzometry

strain gages

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Micro-mechanical accelerometer - also for air bag system

- fabricated by MEMS technology (microsensor)

a

UA

UA

UB

UB

UC

UC

NS

0V

0V

ZSD

G1MHz

R

NO

C DP

REF

4m

2 5 3

1

- platform plate made from polycrystalic Si

- 2 bow strings anchored on polycrystalic Si substrate

- teeth of comb (seismic mass) = movable central electrodesADXL 02, ADXL 50 .. electrostatically compensated (electromechanical feedback)ADXL 202 .. dual -axis without electromechanical feedback

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Accelerometer with piezoelectric layers- polymer piezoelectric film

Z

Y1

Y2

YZ

-high sensitivity- stability- small dimensions- easy assemblage- cheap

- application: detection of hard disk shaking

Y1, Y 2, Z - beams

- measurement of acceleration of translation movement in direction of X, Z

- measurement of angle acceleration - Y1, Y

2

dMdt

dM)dr (

dt

drM

dt

duu 2

2

B2

2

A2

2

ba

=+

=

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Sensors for inertial navigation- measurement of acceleration vector components in 3 axis by absolutesensors, then double integration of the output signals

Note : angular rate sensors often (wrongly) knownas gyros - not the same as real gyroscopes

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Sensors for inertial navigation- measurement of acceleration vector components in 3 axis by absolutesensors, then double integration of the output signals

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Resonant micro-accelerometer

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Sensor of angular velocity based on Coriolis force

R

KD

Z

i

Uv

Vd

Vn

v r

= r vm2F

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-Dual Axis Angular Rate Sensor (Berkeley)Min 1.2/sec, 20Hz bandwidth

-Butterfly-Gyro (SensoNor)(fork gyro)approximately 0.1 /sec at 50 Hz bandwidth

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Gyros with vibrating ring

Scanning Electron Photomicrograph of thesensor

(YAZDI N., AYAZI F., NAJAFI K)

(DELPHI INTELLEK)

Accelerometers with electromechanical

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Accelerometers with electromechanicalfeedback (servo-accelerometers)

k

k

x(t)

m

y(t)M

2

4

3

1

5

6

1

2

C M ic obvodkapacitnho

snma e

Zesilova

u R

3

i

b)

c)a)

1 - electrodesmeasuring circuit

4 - coil3 - magnet2 elastic elements b)

c) detailed view of

elastic elementsLinearity 0.01 %, reproducibility 5*10 -4 g for FS = 50 g, resolution 1 g

Air planes

missiles

inclinometers

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2. Relative sensors of vibrations

)t(F)yx(k dt

)yx(d b

dtxd

m 22

=+

+

y(t) = konst

- condition for preserving permanent mechanicalcontact of sensor tip

01

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2. Relative sensors of vibrations

model of relativesensor of vibrations

222

2

s )B2()1(k ) j(F) j(X

+

=

)t(F)yx(k dt)yx(d

bdtxd

m 22

=+

+

k )t(F

xdtdx

k b

dtxd

k m s

2

2

=++

y(t)=konst

- amplitude frequency response.:

- phase frequency response.:

21B2

arctg

= - condition for proper operation

- hopping of the tip when not fulfilled

1

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Mechanical filters for accelerometers

- Problem: saturation of amplifier = consequence of shocks, shaking, and otherhigh frequency vibrations beyond the useful range- Workaround: mechanical filtering

akcelerometr butylovguma

a(t)

butylrubber